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arXiv · 2112.08420

On the properties of functions of the Takagi power class

O. E. Galkin·S. Yu. Galkina·A. A. Tronov
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Abstract

By construction, functions of Takagi power class are similar to Takagi's continuous nowhere differentiable function. These functions have one real parameter $p>0$. They are defined by the series $S_p(x) = \sum_{n=0}^\infty (T_0(2^nx)/2^n)^p$, where $T_0(x)$ is the distance from the real number $x$ to the nearest integer. We study such properties of functions $S_p(x)$ as continuity, generalized H\"older condition, global maxima and differentiability at the points $x=1/3$ and $x=2/3$, for various values of $p$.

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O. E. Galkin, S. Yu. Galkina, A. A. Tronov. 2021-12-15. On the properties of functions of the Takagi power class. https://arxiv.org/abs/2112.08420

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